The evolution of a binary in a retrograde circular orbit embedded in an accretion disk^⋆

¹ DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
e-mail: pbi20@cam.ac.uk
² Astro Space Centre, P. N. Lebedev Physical Institute, 84/32 Profsoyuznaya st., 117997 Moscow, Russia
³ Astronomy Unit, Queen Mary University of London, Mile end Road, London, E1 4NS, UK

Received: 9 June 2014
Accepted: 8 October 2014

Abstract

Aims. Supermassive black hole binaries may form as a consequence of galaxy mergers. Both prograde and retrograde orbits have been proposed. We study a binary with a small mass ratio, q, in a retrograde orbit immersed in and interacting with a gaseous accretion disk in order to estimate the time scales for inward migration that leads to coalescence and the accretion rate to the secondary component.

Methods. We employed both semi-analytic methods and two-dimensional numerical simulations, focusing on the case where the binary mass ratio is small but large enough to significantly perturb the disk.

Results. We develop the theory of type I migration in this case and go on to determine the conditions for gap formation. We find that when this happens inward migration occurs on a time scale equal to the time required for one half of the secondary mass to be accreted through the unperturbed accretion disk. The accretion rate onto the secondary itself is found to only play a minor role in the orbital evolution as it is of the order of q^1/3 of that to the primary. We obtain good general agreement between the semi-analytic and fully numerical approaches and note that the former can be applied to disks with a wide dynamic range on long time scales.

Conclusions. We conclude that inward migration induced by interaction with the disk can enable the binary to migrate inwards, alleviating the so-called final parsec problem. When q is sufficiently small, there is no well-pronounced cavity inside the binary orbit, unlike the prograde case. The accretion rate to the secondary does not influence the binary orbital evolution much, but can lead to some interesting observational consequences, provided the accretion efficiency is sufficiently large. In this case the binary may be detected as, for example, two sources of radiation rotating around each other. However, the study should be extended to consider orbits with significant eccentricity and the effects of gravitational radiation at small length scales. Also, torques acting between a circumbinary accretion disk, which has a non-zero inclination with respect to a retrograde binary orbit at large distances, may cause the inclination to increase on a time scale that can be similar to, or smaller than, the time scale of orbital evolution, depending on the disk parameters and binary mass ratio. This is also an aspect for future study.